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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 551 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.2x − 2y = −8 and 3x + y = 8 →
  2. 2.4x + 2y = 26 and x − 3y = −11 →
  3. 3.7x + 2y = −38 and 2x + 7y = 2 →
  4. 4.3x + y = 6 and x + 3y = 10 →
  5. 5.3x − y = −13 and 2x − 3y = −4 →
  6. 6.7x + 3y = −41 and 3x + 7y = 11 →
  7. 7.7x + 6y = 55 and 6x + 7y = 49 →
  8. 8.2x + 9y = 0 and 9x + 2y = −77 →
  9. 9.x − 2y = −12 and 2x + 6y = 56 →
  10. 10.8x + 9y = 26 and 9x + 8y = 25 →
  11. 11.9x + 6y = −36 and 6x + 9y = −9 →
  12. 12.x + 9y = −26 and 9x + y = 6 →
  13. 13.4x + 2y = −10 and 2x − y = −11 →
  14. 14.x + 4y = −3 and 5x + 5y = 0 →
  15. 15.8x + 5y = −59 and 5x + 8y = −32 →
  16. 16.6x − y = 36 and 4x + y = 14 →
  17. 17.7x + 2y = −57 and 2x + 7y = 3 →
  18. 18.4x + 7y = −10 and 7x + 4y = −34 →
  19. 19.6x + 2y = 14 and x + 6y = −43 →
  20. 20.6x + y = 13 and 6x − 4y = −22 →
  21. 21.x + 2y = −1 and 2x + y = −11 →
  22. 22.5x − y = 33 and 4x + 2y = 32 →
  23. 23.6x + y = 4 and x + 6y = −11 →
  24. 24.6x + 5y = −6 and 6x + y = −30 →
  25. 25.x + 2y = −4 and 5x + y = 16 →
  26. 26.x + 2y = −15 and 2x + y = −21 →
  27. 27.5x − 3y = 37 and 3x + 5y = −39 →
  28. 28.6x + y = −44 and 3x − 5y = 22 →
  29. 29.6x + 2y = 58 and 2x + 6y = 30 →
  30. 30.x − 4y = −42 and 5x + 6y = 24 →
  31. 31.8x + 2y = 14 and 2x + 8y = −34 →
  32. 32.2x + 9y = −10 and 9x + 2y = 32 →
  33. 33.3x + 6y = −48 and 6x + 3y = −51 →
  34. 34.3x + y = 4 and 4x − 3y = 1 →
  35. 35.2x + 5y = 31 and 5x + 2y = 46 →
  36. 36.8x + 9y = 105 and 9x + 8y = 99 →
  37. 37.6x + 3y = 9 and 6x − 2y = 14 →
  38. 38.2x + 4y = 42 and 2x + 6y = 54 →
  39. 39.3x + 3y = 12 and 5x + 6y = 28 →
  40. 40.5x + 9y = 22 and 9x + 5y = 62 →

Answer key

  1. x = 1, y = 5
  2. x = 4, y = 5
  3. x = −6, y = 2
  4. x = 1, y = 3
  5. x = −5, y = −2
  6. x = −8, y = 5
  7. x = 7, y = 1
  8. x = −9, y = 2
  9. x = 4, y = 8
  10. x = 1, y = 2
  11. x = −6, y = 3
  12. x = 1, y = −3
  13. x = −4, y = 3
  14. x = 1, y = −1
  15. x = −8, y = 1
  16. x = 5, y = −6
  17. x = −9, y = 3
  18. x = −6, y = 2
  19. x = 5, y = −8
  20. x = 1, y = 7
  21. x = −7, y = 3
  22. x = 7, y = 2
  23. x = 1, y = −2
  24. x = −6, y = 6
  25. x = 4, y = −4
  26. x = −9, y = −3
  27. x = 2, y = −9
  28. x = −6, y = −8
  29. x = 9, y = 2
  30. x = −6, y = 9
  31. x = 3, y = −5
  32. x = 4, y = −2
  33. x = −6, y = −5
  34. x = 1, y = 1
  35. x = 8, y = 3
  36. x = 3, y = 9
  37. x = 2, y = −1
  38. x = 9, y = 6
  39. x = −4, y = 8
  40. x = 8, y = −2

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